Real-world models for multiple term structures: a unifying HJM semimartingale framework

TL;DR

This paper introduces a comprehensive HJM-based framework for modeling multiple term structures across various markets, analyzing market viability, and solving related SPDEs for better financial modeling.

Contribution

It unifies the modeling of multiple term structures within a single HJM semimartingale framework under the real-world measure, including SPDE analysis.

Findings

Characterized the set of local martingale deflators.

Proved existence and uniqueness of solutions to the SPDE.

Analyzed invariance properties and affine realizations.

Abstract

We develop a unified framework for modeling multiple term structures arising in financial, insurance, and energy markets, adopting an extended Heath-Jarrow-Morton (HJM) approach under the real-world probability. We study market viability and characterize the set of local martingale deflators. We conduct an analysis of the associated stochastic partial differential equation (SPDE), addressing existence and uniqueness of solutions, invariance properties and existence of affine realizations.